Korringa behavior

Fig, 19. H-NMR relaxation rate l/Tj of K (BEDT-TTF-hg)2Cu(NCS)2 at low temperatures. The broken line indicates the Korringa behavior determined at high temperatures. 

In metals 4f ions are much better ESR probes than 3d ions due to fact that the exchange parameter Jie is about ten times smaller for the exchange interactions between 4f electrons and the band states. The solubility of the 4f ions in many metallic elements is sufficient to perform ESR experiments and at least at low temperatures, narrow absorption lines can be expected. In most cases line positions and linewidths are determined by CF effects in addition to the well-known Korringa behavior. Again the ions with an S ground state like Gd " and Eu " are the preferred probes for ESR investigations. They warrant small crystalline-field influences on the linewidth and on the resonance field. This is the reason that by far most of the publications deal with Gd ". ... 

Larica and Guimareas (1976) investigated the intermetallic compounds GdAgi-iIn c (0 < X < 0.6). The linewidths show a Korringa behavior above a certain temperature, Tminj with a slope b which scarcely depends on x. However, Tmin depends on x. At Tmin the linewidth passes through a minimum 380-750 G) and rises again towards... 

Fig. 51. Temperature dependence of the Gd-ESR linewidth in URu Sij for different Gd concentrations. The experiments have been performed on grain-oriented samples. The solid line indicates the heavy-Fermi liquid-like Korringa behavior. The inset shows A// vs. r in the vicinity of the AFM phase transition for two orientations. From Spitzfaden et al. (1996).

Unlike CO adsorbed onto supported Ru nanopartieles, CO adsorbed on Ru-black showed a large isotropic shift and a symmetric broadening of the NMR spectrum. In all these catalysts, the spin-lattice relaxation time (Tl) has followed the Korringa behavior characteristic of metallic systems [179]. Thus, CO adsorbed on Pt/Ru catalysts attains metallic properties due to the mixing of CO molecular orbitals with the conduction electron states of the transition metal. This observation strongly suggests that the electronic influence of Ru on surface Pt atoms is only a local effect, and Pt atoms situated away from Ru sites retain their original electronic band structure properties. 

The eneigy dependence of the quasielastic scattering may best be analyzed in terms of a single LorentziaiL The temperature dependenee of this linewidth is shown in fig. 32 (solid circles). The lower solid line represents qualitatively the Korringa behavior of a stable... 

Fig. 32. The quasielaslic linewidth of CePdj and Smo75Y 25S as function of temperature. Data taken from Holland-Moritz et al. (1982) (solid circles), Galera et al. (1987) (open circles), and Weber et al. (1989a) (solid squares). The dashed arrow at 7 = 30K represents a lower limit of T/2 expected from the cold neutron scattering experiment. The thick solid line represents r/2 = k 7 and the solid line at the bottom the Korringa behavior.

Perhaps not surprisingly, the most thorough NMR studies of Knight shifts, Korringa relaxation, metal-insulator transitions, and the NMR of the dopant nuclei themselves have been carried out for doped silicon. Since few semiconductors other than PbTe, which presents a considerably more complicated case, have been studied in such detail, it is worthwhile here to summarize salient points from these studies. They conveniently illustrate a number of points, and can shed light on the behavior to be expected in more contemporary studies of compound semiconductors, which are often hindered by the lack of availability of a suite of samples of known and widely-varying carrier concentrations. 

The second argument offered in [359] was based on the observation of 71Ga / j 1 rates at different temperatures that were faster than those calculated assuming Korringa relaxation as the only mechanism. However, this observation cannot be used to exclude the presence of Korringa relaxation, since additional mechanisms can always contribute additively to relaxation rates. Indeed, exactly such behavior has been observed for 71Ga MAS-NMR of h-GaN co-doped with Ge and Mn, where... 

The main result extracted from P NMR was that the AU55 clusters do not exhibit a normal Korringa relation. Rather, there is an indication of the sort of general two-level behavior often seen in disordered glassy systems. This does not appear to be in disagreement with the results reported above, especially when one considers the modification of the intra-cluster energy levels due to the intercluster interactions. 

Experimentally, a metal-insulator transition has been observed between 8 and 12 kbar in Rb4C60 through NMR [44]. This is illustrated in Fig. 17 by the temperature dependence of 1IT1 for different pressures. While the behavior at 1 bar is dominated by an activated component, very similar to the one of K4C60 in Fig. 14, it gradually evolves towards a linear behavior, which is characteristic of a metal. This is the so-called Korringa law where the slope is proportional to n(E )2. Remarkably, the pressure needed to close the gap is quite modest, consistent with the idea that the indirect gap in the band structure could indeed be quite small. To date, this is the only report about such a transition. 

The temperature dependence of the NMR relaxation rate Tf1 for the Au compound (Fig. 9) exhibits a typical behavior of one-dimensional conductors with deviations to the Korringa law (Tf1 T) shown by the upward curvature at high temperatures similarly to (TMTTF)2PF6 [41] and TTF[Ni(dmit)2] [42]. Since there are no localized spins on the dithiolate chain, the relaxation comes from the hyperfine contact and dipolar interactions, 7 1 + r j, produced by the spins of the itinerant electrons along the perylene stacks. The enhancement of the relaxation is, however, less important than that shown by the Bechgaard salts [45]. 

In Fig. 9, Tf1 is represented as a function of temperature for the Au and Pt compounds. As mentioned above, the Au Tf1 value is reminiscent of one-dimensional conductors with deviations of the Korringa law. In the Pt compound Tr1 is temperature independent above 30 K, this behavior being attributed to localized spins. Below 30 K there are deviations of the Curie-Weiss law that affect T71. It is interesting to note that Tf1 Txs(T) over the entire temperature range. From the other properties of this compound the main contribution to Tf1 is considered to be the T d term since the contact term should be negligible. 

The quasiplateau for Tf1 which is observed for C104 and also for PF6 salts under pressure (Fig. 10b) is therefore related to 2kF correlations in a transient temperature regime when the nesting vector evolves from a purely one-dimensional situation (2fcF,0) to a vector that provides the best nesting of the two (three)-dimensional Fermi surface. Below the crossover temperature Tx a Fermi liquid behavior is recovered with an enhanced Korringa... 

This is clear for a macroscopic (even if not semi-infinite) crystal, but we may wonder about the limit in size to which it will remain valid What is the work function of a nanocrystal For a molecule, there is a difference between the amount of work required to pull an electron off (the ionization energy) and the work gained by pushing an extra electron on (the electron affinity). As a condition for the application of the work function concept we may require that the ionization energy of the system be reasonably nearly equal to its electron affinity (it is of course easier to propose the criterion than to verify it experimentally). In this chapter, I frequently use the existence of a Korringa-type of spin lattice relaxation, or that of a conspicuous Knight shift, as a criterion for metalhc behavior, but this is not quite the same as the ionization/affinity criterion. 

Fk . 22. Spin lattice relaxation rate Tl of II in bulk Pdll, with x in the 0.7 to 0.8 range as a function of temperature and for several Larmor frequencies vo The straight line indicates a temperature-independent Korringa product TiT. characteristic of metallic behavior there is a nonzero LDOS on the H at the Fermi energy, in qualitative agreement with Fig. 21b. [Reproduced with permission from Schoep el al (68). Copyright 1974 Filsevier Science.]... 

As shown in Fig. 12, another regime of relaxation is reached at very low temperature (7 <8 K), where a behavior l/T, oc Tis recovered [51, 69, 70, 144]. The low temperature regime looks like a Korringa law with an enhancement factor of the order 10 with respect to the regime r>30 K. It has been first proposed that this change in behavior for the enhancement originates in the dimensionality cross-over of one-particle coherence and the restoration of a Fermi liquid component in two directions. It is still an open problem to decide whether the Fermi liquid properties recovered below 8 K are those of a 2-D or 3-D electron gas. Furthermore the intermediate temperature regime 8 K ... 

Other experimental method at a eomparable level of detail, although in some eases the conclusions reached support previous work by XANES using synchrotron radiation. Our results clearly demonstrate that due to a quantum mechanical electron density spillover from platinum, the interface is metallized, as evidenced by Korringa relaxation and Knight shift behavior. Thus, the adsorbate on a platinum electrode belongs to the metal part of the platinum-solution interface, and most likely other d-metal interfaces, and should be considered as such in any realistic models of the structure of the electrical double layer of interest to electrocatalysis. 

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